A REFINED SHEAR DEFORMATION PLATE THEORY FOR STATIC AND FREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED PLATES

Yıl 2018, Cilt: 8 Sayı: 2, 142 - 144, 30.11.2018

Hamidi Ahmed Zidour Mohamed Sadoune Mohamed

Öz

In this
research, an efficient shear deformation plate theory  for a 
functionally graded  plate  has been investigated by the use of the new
four variable refined plate theory. Unlike any other theory, the number of
unknown functions involved is only four, as against five in case of other shear
deformation theories. The theory account for higher-order variation of
transverse shear strain through the depth of the plate and satisfies the zero
traction boundary conditions on the surfaces of the plate without using shear
correction factors. Based on the 
present  higher-order  shear 
deformation  plate  theory, 
the  equations  of 
the  motion  are derived 
from  Hamilton’s  principal. The plate faces are assumed to
have isotropic, two-constituent material distribution through the thickness,
and the modulus of elasticity, Poisson’s ratio of the faces, and thermal
expansion coefficients are assumed to vary according to a power law
distribution in terms of the volume fractions of the constituents. The validity
of the present theory is investigated by comparing some of the present results
with those of the classical, the first-order and the other higher-order
theories. The influences played by the transverse shear deformation, aspect
ratio, side-to-thickness ratio, and volume fraction distribution are studied.
Numerical results for deflections and stresses of functionally graded plate are
investigated.

Anahtar Kelimeler

Functionally graded material, Static Analysis, Vibration Analysis, Modeling, Bending

A REFINED SHEAR DEFORMATION PLATE THEORY FOR STATIC AND FREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED PLATES

Öz

In this
research, an efficient shear deformation plate theory  for a 
functionally graded  plate  has been investigated by the use of the new
four variable refined plate theory. Unlike any other theory, the number of
unknown functions involved is only four, as against five in case of other shear
deformation theories. The theory account for higher-order variation of
transverse shear strain through the depth of the plate and satisfies the zero
traction boundary conditions on the surfaces of the plate without using shear
correction factors. Based on the 
present  higher-order  shear 
deformation  plate  theory, 
the  equations  of 
the  motion  are derived 
from  Hamilton’s  principal. The plate faces are assumed to
have isotropic, two-constituent material distribution through the thickness,
and the modulus of elasticity, Poisson’s ratio of the faces, and thermal
expansion coefficients are assumed to vary according to a power law
distribution in terms of the volume fractions of the constituents. The validity
of the present theory is investigated by comparing some of the present results
with those of the classical, the first-order and the other higher-order
theories. The influences played by the transverse shear deformation, aspect
ratio, side-to-thickness ratio, and volume fraction distribution are studied.
Numerical results for deflections and stresses of functionally graded plate are
investigated.

Anahtar Kelimeler

Functionally graded material, Static Analysis, Vibration Analysis, Modeling, Bending

Kaynakça

• [1] J. N. Reddy, “Analysis of functionally graded plates,” Int. J. Num. Methods Eng., vol. 47, 2000, pp. 663-684. [2] Z.Q. Cheng, R.C. Batra, “Deflection Relationships Between the Homogeneous Kirchhoff Plate Theory and Different Functionally Graded Plate Theories, “Archives of Mechanics, vol. 52, 2000, pp. 143–158. [3] Z.Q. Cheng, R.C. Batra, “Exact Correspondence Between Eigenvalues of Membranes and Functionally Graded Simply Supported Polygonal Plates,” Journal of Sound and Vibration, vol. 229, 2000, pp. 879–895. [4] Z.Q. Cheng, R.C. Batra, “Three-dimensional Thermoelastic Deformations of a Functionally Graded Elliptic Plate,” Composites, Part B, vol. 31, 2000, pp. 97–106. [5] S.S.Vel, R.C. Batra, “Exact Solution for Thermoelastic Deformations of Functionally Graded Thick Rectangular Plates,” AIAA Journal, vol. 40, 2002, pp. 1421–1433.